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I just can't get to like biology.
Literal
Biology [topic-は] like-become-cannot [polite-ません].
好きになる literally is 'to become liked/loved' (with なる on a na-adjective). Add the potential and negate it: 好きになれない 'cannot come to like.' This captures something English handles awkwardly — the inability to develop a taste for something, distinct from simply disliking it. The sentence reflects an honest attempt that hasn't worked, not active dislike.